Stochastic H∞ identification: an iteratively weighted least squares algorithm

We present a novel problem formulation and algorithm for H^∞ system identification based on a stochastic noise model and constrained model set to reduce the conservatism in deterministic noise models, and statistical inefficiency and computational complexity associated with high-order estimates. By establishing a connection between a minimax problem and a sequence of weighted least square problems, we show that the proposed stochastic, constrained problem can be solved with a computationally attractive and conceptually simple iteratively weighted least square (IWLS) identification algorithm. The IWLS procedure is based on a sequence of standard parametric weighted least square output error identification routines, where the weighting is updated via nonparametric estimation of the modeling error to asymptotically achieve the H^∞ identification criterion